{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f05106bb",
   "metadata": {},
   "source": [
    "## 快速傅里叶变化\n",
    "\n",
    "1. 多项式的两种表达方式\n",
    "2. 多项式的和与积\n",
    "3. 复数的单位根\n",
    "4. 离散傅里叶变换\n",
    "5. 快速傅里叶变换"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2a9b72e9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## 复数单位根\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plot\n",
    "plot.axes(projection = 'polar')\n",
    "plot.title(' Cicle in polar format: r=R')\n",
    "rads = np.arange(0, (2*np.pi), 2*np.pi / 8)\n",
    "for radian in rads:\n",
    "    plot.polar(radian, 1, 'o')\n",
    "plot.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "58011c5e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## 构造n次方根\n",
    "import math\n",
    "import cmath\n",
    "import matplotlib.pyplot as plt\n",
    "def create_n_complex_roots(n):\n",
    "    nth_roots = []\n",
    "    for k in range(n):\n",
    "        w_k = complex(math.cos(2*k*np.pi / n), math.sin(2*k*np.pi /n))\n",
    "        nth_roots.append(w_k)\n",
    "    return nth_roots\n",
    "\n",
    "nth_roots = create_n_complex_roots(16)\n",
    "polar = []\n",
    "for root in nth_roots:\n",
    "    polar.append(cmath.polar(root))\n",
    "for r in polar:\n",
    "    plt.polar(r[1], r[0], 'o')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "3ad451ce",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "polynominal coefficients are: [0 1 2 3 4 5 6 7]\n",
      "fast fourier results are : [(28+0j), (-4-9.65685424949238j), (-4-4j), (-4-1.6568542494923797j), (-4+0j), (-4+1.6568542494923806j), (-3.9999999999999996+4j), (-3.9999999999999987+9.65685424949238j)]\n"
     ]
    }
   ],
   "source": [
    "def fast_fourier_transform(coefficients):\n",
    "    if len(coefficients) <= 1:\n",
    "        return coefficients\n",
    "    \n",
    "    degree = len(coefficients)\n",
    "    n_complex_roots = create_n_complex_roots(degree)\n",
    "    event_coefficients = coefficients[0 : degree: 2]\n",
    "    odd_coefficients = coefficients[1 : degree: 2]\n",
    "\n",
    "    event_fft = fast_fourier_transform(event_coefficients)\n",
    "    odd_fft = fast_fourier_transform(odd_coefficients)\n",
    "\n",
    "    fft_first_part = []\n",
    "    fft_second_part = []\n",
    "\n",
    "    for k in range(0, int(degree / 2)):\n",
    "        w = n_complex_roots[k]\n",
    "        fft_first_part.append(event_fft[k] + w * odd_fft[k])\n",
    "        fft_second_part.append(event_fft[k] - w * odd_fft[k])\n",
    "\n",
    "    fft = []\n",
    "    fft.extend(fft_first_part)\n",
    "    fft.extend(fft_second_part)\n",
    "    return fft\n",
    "\n",
    "degree = 8\n",
    "coefficients = np.arange(degree)\n",
    "print(\"polynominal coefficients are:\", coefficients)\n",
    "fft_results = fast_fourier_transform(coefficients)\n",
    "print(\"fast fourier results are :\", fft_results)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "env_py38",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.18"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
